OFDM is a powerful modulation format over frequency-selective radio channels. Low complexity equalization, robustness for frequency selective channels, and the ability to use different data modulations on different sub-carriers are the main advantages of OFDM. OFDM systems are, however, also known to be sensitive to phase-noise; a radio-hardware imperfection that causes the OFDM sub-carriers to become non-orthogonal. Due to the resulting inter-sub-carrier interference, ICI, the demodulator signal-to-noise plus interference ratio, SINR, is reduced. If the phase noise process can be estimated, its negative effect on receiver performance can partly be compensated for by digital signal processing at the receiver.
In principle, phase noise estimation is performed at the receiver by observing the change in carrier-phase between the received symbols and a sequence of known phase reference symbols. Various phase estimation techniques exist which can be divided into two main categories. On the one hand, there are reference symbol-based estimators where reference symbols are known a-priori, and on the other hand, decision feedback estimators where tentative decisions on data symbols are made and used as reference symbols in an iterative fashion. It is also possible to combine reference symbol-based and decision feedback based estimators.
In single-carrier schemes it is often a relatively easy task to estimate and compensate for phase noise, as the phase noise process typically is narrowband compared to the modulation bandwidth. In other words, the change in phase from one known reference symbol to the next is typically small enough to be accurately estimated and compensated for. The situation is, however, different in OFDM systems. An OFDM system with N sub-carriers has an N-fold increase in symbol time, compared to a single-carrier system with the same modulation symbol rate1. This can be seen in FIGS. 3A and 3B, where time-frequency diagrams of an OFDM and a single-carrier scheme are illustrated. As N often is a relatively large number there can be a significant change in the phase noise process during one OFDM symbol. As a consequence, to reach acceptable receiver performance it will be necessary to compensate not only for the average phase over each OFDM symbol but also for phase fluctuations during each OFDM symbol. 1 For simplicity we omit the cyclic-prefix here as it typically is short compared to the total OFDM symbol time.
FIGS. 1-2 show schematic block diagrams of a conventional OFDM transmitter and receiver arranged for phase noise estimation and compensation. Key components in the OFDM transmitter and receiver are the inverse discrete Fourier transform, IDFT, and the discrete Fourier transform, DFT. The transmitter, shown in FIG. 1, has data symbols and phase reference symbols as input. The inputs are fed to an OFDM modulator, comprising a serial-to-parallel, S/P, converter for parallelizing the input symbols, an N-point IDFT for mapping N input symbols to N sub-carriers and outputting N time-domain samples, a parallel-to-serial, P/S, converter for serializing the time-domain samples and an insert prefix unit for inserting a cyclic prefix before transmission of the OFDM symbol. The OFDM modulator output is low-pass filtered and converted to continuous time in an LP & DAC unit and passed on to a TX block connected to an antenna for transmission. The TX block comprises radio-hardware, including circuitry for up-converting the baseband signal to a radio frequency, RF, signal. FIG. 2 shows the conventional OFDM receiver arranged for phase estimation and compensation. An RF signal is received at an antenna connected to an RX block. The RX block comprises radio-hardware, including circuitry for down-converting the received RF signal to baseband. The received signal is converted to discrete-time and low-pass filtered in an LP & ADC unit. The discrete-time received signal is input to a phase estimation unit, which computes phase compensation estimates by comparing the received signal with known phase references. The phase compensation estimates are used to compensate the discrete-time received signal before a conventional OFDM demodulator demodulates the phase compensated signal. The OFDM demodulator, comprises a remove prefix unit for removing the time-domain cyclic prefix, a parallel-to-serial, P/S, converter for parallelizing the received time-domain samples, and an N-point DFT configured to obtain the received data symbols.
In the OFDM literature, most phase compensation schemes are targeting estimators and compensation algorithms for standardized OFDM systems, such as IEEE 802.11 and 3GPP LTE. Very few, if any, are targeting the design of reference signals for phase noise estimation in applications where phase noise is the limiting factor. Reference R1 provides an overview of state-of-the-art phase noise estimation and mitigation techniques. The most basic techniques are based on common phase error, CPE, estimation and compensation for all sub-carriers. However, CPE-based compensation algorithms have the same effect on all sub-carriers inside one OFDM symbol and will therefore not mitigate ICI. More advanced ICI reduction techniques range from fairly simple interpolation between consecutive CPE-estimates to more advanced MMSE estimators or iterative methods.
However, the above methods do not provide sufficient ICI mitigation in OFDM systems operating under severe phase noise. For example, OFDM has previously not been suitable for applications such as microwave radio backhaul where phase noise is often the most performance-limiting factor. Hence, there is a need to design a phase reference symbol format to be used for phase synchronization in OFDM systems where phase noise is the limiting factor.    [R1] V. Syrjälä, M. Valkama, N. Tchamov, and J. Rinne, “Phase Noise Modelling and Mitigation Techniques in OFDM Communications Systems”, in Proc. IEEE WTS 09, pp. 1-7, April 2009.